Stochastic Local Search Methods Research Articles

Generalization and completeness of stochastic local search algorithms

We generalize Stochastic Local Search (SLS) heuristics into a unique formal model. This model has two key components: a common structure designed to be as large as possible and a parametric structure intended to be as small as possible. Each heuristic is obtained by instantiating the parametric part in a different way. Particular instances for Genetic Algorithms (GA), Ant Colony Optimization (ACO), and Particle Swarm Optimization (PSO) are presented. Then, we use our model to prove the Turing-completeness of SLS algorithms in general. The proof uses our framework to construct a GA able to simulate any Turing machine. This Turing-completeness implies that determining any non-trivial property concerning the relationship between the inputs and the computed outputs is undecidable for GA and, by extension, for the general set of SLS methods (although not necessarily for each particular method). Similar proofs are more informally presented for PSO and ACO.

Stochastic local search: a state-of-the-art review

The main objective of this paper is to provide a state-of-the-art review, analyze and discuss stochastic local search techniques used for solving hard combinatorial problems. It begins with a short introduction, motivation and some basic notation on combinatorial problems, search paradigms and other relevant features of searching techniques as needed for background. In the following a brief overview of the stochastic local search methods along with an analysis of the state-of-the-art stochastic local search algorithms is given. Finally, the last part of the paper present and discuss some of the most latest trends in application of stochastic local search algorithms in machine learning, data mining and some other areas of science and engineering. We conclude with a discussion on capabilities and limitations of stochastic local search algorithms.

A Stochastic Local Search Algorithm for the Partial Max-SAT Problem Based on Adaptive Tuning and Variable Depth Neighborhood Search

The Partial Max-SAT (PMSAT) problem is an optimization variant of the well-known Propositional Boolean Satisfiability (SAT) problem. It holds an important place in theory and practice, because a huge number of real-world problems, such as timetabling, planning, routing, bioinformatics, fault diagnosis, etc., could be encoded into it. Stochastic local search (SLS) methods can solve many real-world problems that often involve large-scale instances at reasonable computation costs while delivering good-quality solutions. In this work, we propose a novel SLS algorithm called adaptive variable depth SLS for PMSAT problem solving based on a dynamic local search framework. Our algorithm exploits two algorithmic components of an SLS method: parameter tuning and neighborhood search. Our first contribution is the design of an adaptive parameter tuner that searches for the best parameter setting for each instance by considering its features. The second contribution is a variable depth neighborhood search (VDS) algorithm adopted for PMSAT problem, which our empirical evaluation proves is a more efficient w.r.t. single neighborhood search. We conducted our experiments on the PMSAT benchmarks from MaxSAT Evaluation 2014 to 2019, including more than 3600 instances which have been encoded from a broad range of domains such as verification, optimization, graph theory, automated-reasoning, pseudo Boolean, etc. Our experimental evaluation results show that AVD-SLS solver, which is implemented based on our algorithm, outperforms state-of-the-art PMSAT SLS solvers in most benchmark classes, including random, crafted, and industrial instances. Furthermore, AVD-SLS reports remarkably better results on weighted benchmark, and shows competitive results with several well-known hybrid PMSAT solvers.

Stochastic local search for Partial Max-SAT: an experimental evaluation

Stochastic local search (SLS) methods are heuristic-based algorithms that have gained in popularity for their efficiency and robustness when solving very large and complex problems from various areas of artificial intelligence. This study aims to gain insights into SLS methods for solving the Partial Max-SAT (PMSAT) problem. The PMSAT is an NP-Hard problem, an optimization variant of the Propositional Boolean Satisfiability (SAT) problem, that has importance in theory and practice. Many real-world problems including timetabling, scheduling, planning, routing, and software debugging can be reduced to the PMSAT problem. Modern PMSAT solvers are able to solve practical instances with hundreds of thousands to millions of variables and clauses. However, performance of PMSAT solvers are still limited for solving some benchmark instances. In this paper, we present, investigate, and analyze state-of-the-art SLS methods for solving the PMSAT problem. An experimental evaluation is presented based on the MAX-SAT evaluations from 2014 to 2019. The results of this evaluation study show that the currently best performing SLS methods for the PMSAT problem fall into three categories: distinction-based, configuration checking-based, and dynamic local search methods. Very good performance was reported for the dynamic local search based method. The paper gives a detailed picture of the performance of SLS solvers for the PMSAT problem, aims to improve our understanding of their capabilities and limitations, and identifies future research directions.

Automatic design of hybrid stochastic local search algorithms for permutation flowshop problems

Stochastic local search methods are at the core of many effective heuristics for tackling different permutation flowshop problems (PFSPs). Usually, such algorithms require a careful, manual algorithm engineering effort to reach high performance. An alternative to the manual algorithm engineering is the automated design of effective SLS algorithms through building flexible algorithm frameworks and using automatic algorithm configuration techniques to instantiate high-performing algorithms. In this paper, we automatically generate new high-performing algorithms for some of the most widely studied variants of the PFSP. More in detail, we (i) developed a new algorithm framework, EMILI, that implements algorithm-specific and problem-specific building blocks; (ii) define the rules of how to compose algorithms from the building blocks; and (iii) employ an automatic algorithm configuration tool to search for high performing algorithm configurations. With these ingredients, we automatically generate algorithms for the PFSP with the objectives makespan, total completion time and total tardiness, which outperform the best algorithms obtained by a manual algorithm engineering process.

Deterministic Search Methods for Computational Protein Design.

One main challenge in Computational Protein Design (CPD) lies in the exploration of the amino-acid sequence space, while considering, to some extent, side chain flexibility. The exorbitant size of the search space urges for the development of efficient exact deterministic search methods enabling identification of low-energy sequence-conformation models, corresponding either to the global minimum energy conformation (GMEC) or an ensemble of guaranteed near-optimal solutions. In contrast to stochastic local search methods that are not guaranteed to find the GMEC, exact deterministic approaches always identify the GMEC and prove its optimality in finite but exponential worst-case time. After a brief overview on these two classes of methods, we discuss the grounds and merits of four deterministic methods that have been applied to solve CPD problems. These approaches are based either on the Dead-End-Elimination theorem combined with A* algorithm (DEE/A*), on Cost Function Networks algorithms (CFN), on Integer Linear Programming solvers (ILP) or on Markov Random Fields solvers (MRF). The way two of these methods (DEE/A* and CFN) can be used in practice to identify low-energy sequence-conformation models starting from a pairwise decomposed energy matrix is detailed in this review.

Analysis of stochastic local search methods for the unrelated parallel machine scheduling problem

AbstractThis work addresses the unrelated parallel machine scheduling problem with sequence‐dependent setup times, in which a set of jobs must be scheduled for execution by one of the several available machines. Each job has a machine‐dependent processing time. Furthermore, given multiple jobs, there are additional setup times, which vary based on the sequence and machine employed. The objective is to minimize the schedule's completion time (makespan). The problem is NP‐hard and of significant practical relevance. The present paper investigates the performance of four different stochastic local search (SLS) methods designed for solving the particular scheduling problem: simulated annealing, iterated local search, late acceptance hill‐climbing, and step counting hill‐climbing. The analysis focuses on design questions, tuning effort, and optimization performance. Simple neighborhood structures are considered. All proposed SLS methods performed significantly better than two state‐of‐the‐art hybrid heuristics, especially for larger instances. Updated best‐known solutions were generated for 901 of the 1000 large benchmark instances considered, demonstrating that particular SLS methods are simple yet powerful alternatives to current approaches for addressing the problem. Implementations of the contributed algorithms have been made available to the research community.

A hybrid algorithmic model for the minimum weight dominating set problem

Iterated greedy algorithms belong to the class of stochastic local search methods. They are based on the simple and effective principle of generating a sequence of solutions by iterating over a constructive greedy heuristic using destruction and construction phases. This paper, first, presents an efficient randomized iterated greedy approach for the minimum weight dominating set problem, where—given a vertex-weighted graph—the goal is to identify a subset of the graphs’ vertices with minimum total weight such that each vertex of the graph is either in the subset or has a neighbor in the subset. Our proposed approach works on a population of solutions rather than on a single one. Moreover, it is based on a fast randomized construction procedure making use of two different greedy heuristics. Secondly, we present a hybrid algorithmic model in which the proposed iterated greedy algorithm is combined with the mathematical programming solver CPLEX. In particular, we improve the best solution provided by the iterated greedy algorithm with the solution polishing feature of CPLEX. The simulation results obtained on a widely used set of benchmark instances shows that our proposed algorithms outperform current state-of-the-art approaches.

Amoeba-Inspired Heuristic Search Dynamics for Exploring Chemical Reaction Paths.

We propose a nature-inspired model for simulating chemical reactions in a computationally resource-saving manner. The model was developed by extending our previously proposed heuristic search algorithm, called “AmoebaSAT [Aono et al. 2013],” which was inspired by the spatiotemporal dynamics of a single-celled amoeboid organism that exhibits sophisticated computing capabilities in adapting to its environment efficiently [Zhu et al. 2013]. AmoebaSAT is used for solving an NP-complete combinatorial optimization problem [Garey and Johnson 1979], “the satisfiability problem,” and finds a constraint-satisfying solution at a speed that is dramatically faster than one of the conventionally known fastest stochastic local search methods [Iwama and Tamaki 2004] for a class of randomly generated problem instances [http://www.cs.ubc.ca/~hoos/5/benchm.html]. In cases where the problem has more than one solution, AmoebaSAT exhibits dynamic transition behavior among a variety of the solutions. Inheriting these features of AmoebaSAT, we formulate “AmoebaChem,” which explores a variety of metastable molecules in which several constraints determined by input atoms are satisfied and generates dynamic transition processes among the metastable molecules. AmoebaChem and its developed forms will be applied to the study of the origins of life, to discover reaction paths for which expected or unexpected organic compounds may be formed via unknown unstable intermediates and to estimate the likelihood of each of the discovered paths.

Structure-based satisfiability checking

This note summarizes a dissertation that focuses on methods for solving structured real-world problems based on propositional satisfiability (SAT). The work contributes to the analysis and development of both complete search (DPLL and clause learning) and stochastic local search methods for SAT.

Some effective heuristics for no-wait flowshops with setup times to minimize total completion time

In this work, we consider a complex flowshop scheduling problem in which both no-wait and separate setup times are considered. The optimisation criterion is the minimisation of the total completion time. We propose an effective dominance rule for the four machine case that can also be used for m machines. Five simple and fast heuristics are proposed along with two easy to code stochastic local search methods, one of them being based on Iterated Local Search (ILS). An extensive computational evaluation is carried out with two sets of 5,400 instances. All seven methods are compared to two recent algorithms. The results, confirmed by thorough statistical analyses, show that the proposed methods are more effective and efficient when compared to the best existing algorithms in the literature for the considered problem.

Stochastic search versus genetic algorithms for solving real time and over-constrained temporal constraint problems

The aim of this work is to study the applicability of Genetic Algorithms (GAs) and stochastic local search methods to solve real time and over constrained temporal constraint problems. Solving these two type of problems consists of finding a possible